Noncommutative weak Orlicz spaces and martingale inequalities

Volume 204 / 2011

Turdebek N. Bekjan, Zeqian Chen, Peide Liu, Yong Jiao Studia Mathematica 204 (2011), 195-212 MSC: Primary 46L53; Secondary 60G42. DOI: 10.4064/sm204-3-1


This paper is devoted to the study of noncommutative weak Orlicz spaces and martingale inequalities. The Marcinkiewicz interpolation theorem is extended to include noncommutative weak Orlicz spaces as interpolation classes. As an application, we prove the weak type $\varPhi $-moment Burkholder–Gundy inequality for noncommutative martingales through establishing a weak type $\varPhi $-moment noncommutative Khinchin inequality for Rademacher random variables.


  • Turdebek N. BekjanCollege of Mathematics
    and Systems Science
    Xinjiang University
    Urumqi 830046, China
  • Zeqian ChenWuhan Institute of Physics and Mathematics
    Chinese Academy of Sciences
    West District 30
    Xiao-Hong-Shan, Wuhan 430071, China
  • Peide LiuSchool of Mathematics and Statistics
    Wuhan University
    Wuhan 430072, China
  • Yong JiaoInstitute of Probability and Statistics
    Central South University
    Changsha 410075, China

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